We analyse in a systematic way the (non-)compact four dimensional Einstein-Weyl spaces equipped with a Bianchi metric. We show that Einstein-Weyl structures with a Class A Bianchi metric have a conformal scalar curvature of constant sign on the manifold. Moreover, we prove that most of them are conformally Einstein or conformally Kähler ; in the non-exact Einstein-Weyl case with a Bianchi metri...

We analyse in a systematic way the (non-)compact four dimensional Einstein-Weyl spaces equipped with a Bianchi metric. We show that Einstein-Weyl structures with a Class A Bianchi metric have a conformal scalar curvature of constant sign on the manifold. Moreover, we prove that most of them are conformally Einstein or conformally Kahler ; in the non-exact Einstein-Weyl case with a Bianchi metr...

Conformal invariant new forms of p-brane and Dp-brane actions are proposed. These are quadratic in ∂X for the p-brane case and for Dp-branes in the Abelian field strength. The fields content of these actions are: an induced metric, gauge fields, an auxiliary metric and an auxiliary scalar field. The proposed actions are Weyl invariant in any dimension and the elimination of the auxiliary metric...

A massless electroweak theory for leptons is formulated in a Weyl space, W4, yielding a Weyl invariant dynamics of a scalar field φ, chiral Dirac fermion fields ψL and ψR, and the gauge fields κμ, Aμ, Zμ,Wμ and W † μ allowing for conformal rescalings of the metric gμν and all fields with nonvanishing Weyl weight together with the corresponding transformations of the Weyl vector fields, κμ, repr...

Weyl geometry is a natural extension of conformal with covariance mediated by connection. We generalize the Fefferman-Graham (FG) ambient construction for manifolds to corresponding manifolds. first introduce Weyl-ambient metric motivated Weyl-Fefferman-Graham (WFG) gauge. From top-down perspective, we show that space as pseudo-Riemannian induces codimension-2 geometry. Then, from bottom-up sta...

We analyse in a systematic way the four dimensionnal Einstein-Weyl spaces equipped with a diagonal Kähler Bianchi IX metric. In particular, we show that the subclass of EinsteinWeyl structures with a constant conformal curvature is the one with a conformally flat but not necessarily flat metric ; we exhibit its 3-parameter distance and Weyl one-form. This extends previous analysis of Pedersen e...

in this paper, we obtain a necessary and sufficient condition for a conformal mapping between two weyl manifolds to preserve einstein tensor. then we prove that some basic curvature tensors of $w_n$ are preserved by such a conformal mapping if and only if the covector field of the mapping is locally a gradient. also, we obtained the relation between the scalar curvatures of the weyl manifolds r...

We analyse in a systematic way the four dimensionnal Einstein-Weyl spaces equipped with a diagonal Kähler Bianchi IX metric. In particular, we show that the subclass of EinsteinWeyl structures with a constant conformal scalar curvature is the one with a conformally scalar flat but not necessarily scalar flat metric ; we exhibit its 3-parameter distance and Weyl one-form. This extends previous a...

The parent action method is utilized to the Born-Infeld and Dp-brane theories. Various new forms of Born-Infeld and Dp-brane actions are derived by using this systematic approach, in which both the already known 2-metric and newly proposed 3-metric prescriptions are considered. An auxiliary worldvolume tensor field, denoted by ωμν , is introduced and treated probably as an additional worldvolum...

In this paper we classify pseudosymmetric and Ricci-pseudosymmetric (κ, μ)-contact metric manifolds in the sense of Deszcz. Next we characterize Weyl-pseudosymmetric (κ, μ)-contact metric manifolds.